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A Note on Harmonic Functions on surfaces

2014/05/05 by Jean C. Cortissoz, Cortissoz, Jean C.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #msc:58J05

paper · pdf · doi:10.48550/arxiv.1405.0944

Comments and corrections are very welcome! Mistakes and typos found in a previous version have been corrected

arxiv created 2014/08/14 · arxiv updated 2014/08/15

Abstract

We review and give elementary proofs of Liouville type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible growth of harmonic functions when this metric has nonnegative Gaussian curvature.

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